Topology and Spectrum in Measurement-Induced Phase Transitions
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915354281771008 |
|---|---|
| author | Oshima, Hisanori Mochizuki, Ken Hamazaki, Ryusuke Fuji, Yohei |
| author_facet | Oshima, Hisanori Mochizuki, Ken Hamazaki, Ryusuke Fuji, Yohei |
| contents | Competition among repetitive measurements of noncommuting observables and unitary dynamics can give rise to a wide variety of entanglement phases. Here, we propose a general framework based on Lyapunov analysis to characterize topological properties in monitored quantum systems through their spectrum and many-body topological invariants. We illustrate this framework by analyzing (1+1)-dimensional monitored circuits for Majorana fermions, which are known to exhibit topological and trivial area-law entangled phases as well as a critical phase with sub-volume-law entanglement. Through the Lyapunov analysis, we identify the presence (absence) of edge-localized zero modes inside the bulk gap in the topological (trivial) phase and a bulk gapless spectrum in the critical phase. Furthermore, by suitably exploiting the fermion parity with twisted measurement outcomes at the boundary, we construct a topological invariant that distinguishes the two area-law phases and dynamically characterizes the critical phase. Our framework thus provides a general route to extend the notion of bulk-edge correspondence to monitored quantum dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_11097 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Topology and Spectrum in Measurement-Induced Phase Transitions Oshima, Hisanori Mochizuki, Ken Hamazaki, Ryusuke Fuji, Yohei Quantum Physics Disordered Systems and Neural Networks Statistical Mechanics Competition among repetitive measurements of noncommuting observables and unitary dynamics can give rise to a wide variety of entanglement phases. Here, we propose a general framework based on Lyapunov analysis to characterize topological properties in monitored quantum systems through their spectrum and many-body topological invariants. We illustrate this framework by analyzing (1+1)-dimensional monitored circuits for Majorana fermions, which are known to exhibit topological and trivial area-law entangled phases as well as a critical phase with sub-volume-law entanglement. Through the Lyapunov analysis, we identify the presence (absence) of edge-localized zero modes inside the bulk gap in the topological (trivial) phase and a bulk gapless spectrum in the critical phase. Furthermore, by suitably exploiting the fermion parity with twisted measurement outcomes at the boundary, we construct a topological invariant that distinguishes the two area-law phases and dynamically characterizes the critical phase. Our framework thus provides a general route to extend the notion of bulk-edge correspondence to monitored quantum dynamics. |
| title | Topology and Spectrum in Measurement-Induced Phase Transitions |
| topic | Quantum Physics Disordered Systems and Neural Networks Statistical Mechanics |
| url | https://arxiv.org/abs/2412.11097 |